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3 years ago

8

Yoko made $15,000 in taxable income last year. Suppose the income tax rate is 15% for the first $850Cplus 19% for the amount ove

r $8500 How much must Yoko pay in income tax for last year?

1 answer:

Verdich [7]3 years ago

4 0

Answer:

$2510

Step-by-step explanation:

<u>Amount of tax on $8500:</u>

$8500*15/100 = $1275

<u>Amount of income over $8500:</u>

$15000 - $8500 = $6500

<u>Amount of tax on $6500:</u>

$6500*19/100 = $1235

<u>Total tax is:</u>

$1275 + $1235 = $2510

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An aircraft manufacturer wants to determine the best selling price for a new airplane. The company estimates that the initial co

Blizzard [7]

Answer:

$(a)$ $C(x)=500+20x-5x^{\frac{3}{4}}+0.01x^2$

$p(x)=320-7.7p$

$R(x)=(320-7.7p)p=320p-7.7p^2$

$(b)$ $x=82 \text{planes}$

$(c)$ $p=\$30.91 M\;\; \text{per plane}$

$(d)$ maximum profit $=\$ 15.90M$

Step-by-step explanation:

Given that,

The company estimates that the initial cost of designing the aeroplane and setting up the factories in which to build it will be 500 million dollars.

The additional cost of manufacturing each plane can be modelled by the function.

$m(x)=20x-5x^{\frac{3}{4}}+0.01x^2$

$(a)$ Find the cost, demand (or price), and revenue functions.

$C(x)=500+20x-5x^{\frac{3}{4}}+0.01x^2$

$p(x)=320-7.7p$

$R(x)=(320-7.7p)p=320p-7.7p^2$

$(b)$ Find the production level that maximizes profit.

$f=R(x)-C(x)$

$\Rightarrow f=320p-7.7p^2-(500+20x-5x^{\frac{3}{4}}+0.01x^2)$

$\Rightarrow df=320dp-15.4pdp-20dx+5(\frac{3}{4} )x^{\frac{-1}{4} }dx-0.02xdx$

$x=320-7.7p$

$p=\frac{320-x}{7.7}$

$\frac{dp}{dx} = \frac{-1}{7.7}$

$\frac{df}{dx}=\frac{320}{-7.7} -\frac{15.4(320-x) }{7.7(\frac{-1}{7.7} )}-20+5\frac{3}{4} x^{\frac{-1}{4}} -0.02x=0$

$\Rightarrow -41.5584+83.1169-0.2597x-20+3.75x^{\frac{-1}{4} }-0.02x=0$

$\Rightarrow 21.5585+3.75x^{\frac{-1}{4} }-0.279x=0$

$\Rightarrow x=82 \text{planes}$

$(c)$ Find the associated selling price of the aircraft that maximizes profit.

$p=\frac{320-82}{7.7}$

$\Rightarrow p=\$30.91 M\;\; \text{per plane}$

$(d)$ Find the maximum profit.

Manufacturing cost of one plane is:

$m(1)=20-5+0.01$

$=\$15.01 M$

maximum profit $=\$(30.91-15.01)M$

$=\$15.90M$

3 0

3 years ago

Which of the following is the solution to | x | +5< 1?

marissa [1.9K]

C. No Solution

<u>Explanation</u>

<u></u>

The above equation has no solution as the value of x is always mod x which means the value is always positive. Hence to make the equation true, we need value of mod x less than -4 which is not possible. Hence this equation as no solution.

$|x| + 5< 1\\|x| + 5 -1 < 0\\|x| +4 < 0\\|x| < -4$

Since, |x| can never be < -4 because value of |x| is always greater than or equal to, Hence this equation has no solution.

7 0

3 years ago

what is the average speed of a train that covers 80 km in 1 hour, 200 km in 2 hours and 420 kn in 4 hours

omeli [17]

Answer:

95

Step-by-step explanation:

80+(200 divided by 2)+(420 divided by 4)=285

285 divided by 3=95

6 0

3 years ago

How do you write 9.6 x 10 in standard form

motikmotik

since ten isn't to the power of anything it would be just 96

8 0

3 years ago

Please helppp!!!! I’ll give you a crown!!

siniylev [52]

Answer:

the second one

Step-by-step explanation:

the last number of the equation (-3) is the y intercept, so it goes the the point (0,-3), also it has the opposite slope of y=2x-3

i hope this helps and im sorry if im wrong :(

8 0

3 years ago